For example, a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately 1075 mathematical computations per second. If we assume that a cryptographic key can be tested with only one operation, then a typical 128 bit key could be cracked in under 10−36 seconds. However, a 256 bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512 bit key would increase the cracking time to approaching 1072 years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).

The limit has been further analysed in later literature as the maximum rate at which a system with energy spread can evolve into an orthogonal and hence distinguishable state to another, .[3][4] In particular, Margolus and Levitin has shown that a quantum system with average energy E takes at least time to evolve into an orthogonal state.[5]